Are you potentially confusing a page fault which results in the page being pulled into main memory with a cache miss which pulls a line from memory into on-CPU

Are you potentially confusing a page fault which results in the page being pulled into main memory with a cache miss which pulls a line from memory into on-CPU memory? My understanding is that the cache miss is managed by the MMU without much kernel involvement and we're relying on non task aware PMU statistics local to a single CPU for the proposed mitigation. Am I missing some aspect of page mapping/cache management?